The evolution of the salt-water distribution around the Zwin estuary mouth is modeled for a period of about five centuries. The modeled area is situated in the Flemisch coastal plain near the border of The Netherlands and Belgium. The Zwin estuary is the former waterway to the medieval seaports of Bruges and Damme. During the considered period this alluvial estuary silted up and the modeled area changes from an area around a tidal channel, over a mud flat to a rather complex polder dune area. The evolution is simulated by the 3D density depended groundwater flow model MOCDENS3D (Lebbe & Oude Essink, 1999). The row direction of the applied finite-difference grid is parallel to the present coast line. The simulation is based on old paintings and a large number of maps which allow a relatively detailed reconstruction of the evolution of the landscape. The results show the historical evolution of a large number of different inverse density problems in this area

Jonckheere, S.

Lebbe, L.

Vandenbohede, A.

Open Marine Archive

June 23-27, 2008 z Naples, Florida, USA 
141 
Modeling of Historical Evolution of Salt Water Distribution in the Phreatic 
Aquifer in and around the silted up Zwin Estuary Mouth (Flanders, Belgium)   
Luc Lebbe, Sarah Jonckheere and Alexander Vandenbohede 
Department of Geology and Soil Science, Ghent University, Ghent, Belgium 
 
ABSTRACT 
The evolution of the salt-water distribution around the Zwin estuary mouth is modeled for a 
period of about five centuries. The modeled area is situated in the Flemisch coastal plain near the 
border of The Netherlands and Belgium. The Zwin estuary is the former waterway to the 
medieval seaports of Bruges and Damme. During the considered period this alluvial estuary 
silted up and the modeled area changes from an area around a tidal channel, over a mud flat to a 
rather complex polder dune area. The evolution is simulated by the 3D density depended 
groundwater flow model MOCDENS3D (Lebbe & Oude Essink, 1999). The row direction of the 
applied finite-difference grid is parallel to the present coast line. The simulation is based on old 
paintings and a large number of maps which allow a relatively detailed reconstruction of the 
evolution of the landscape. The results show the historical evolution of a large number of 
different inverse density problems in this area. 
 
INTRODUCTION 
To simulate this five hundred years period ten stress periods are considered. Before the 20th 
Century the stresses which influence the groundwater flow and the salt water distribution were 
principally determined by the evolution of the landscape. The simulation starts with the first 
sound representation of the area in a painting of Pourbus (1571). At that time the waterway to the 
seaport Damme ran from the upper right to the lower left corner of the modeled area (Fig. 1). 
This tidal channel was bounded at both sides by relatively flat banks which were temporally 
inundated by sea water depending on the tides. At both sides of the estuary mouth there were 
peninsulas principally existing of dune areas. Behind the western dunes there was a tidal flat area 
with a central gully. During the high waters at spring tides this tidal flat area was completely 
inundated by sea water whereas the sea retreated completely from it at low water. The southern 
boundary of the tidal flat area was bounded by a dyke protecting the polders behind it from 
inundations.  
 
The subsequent stresses on the phreatic aquifer are due to the lateral changes of the landscape 
elements. In the dune area fresh water recharges with a constant rate (280 mm/year). In the tidal 
flat area, the banks of the tidal channel and the shores, the average fresh water head in the 
uppermost layer is derived from the tidal fluctuations and the elevation of the ground surface at 
the treated point. When there is a recharge of groundwater in all the fore mentioned areas the 
water quality corresponds with that of sea water (100% salt water). In the polder areas the top of 
the aquifer is drained at a prescribed level and there is a smaller recharge of water than in the 
dune area. The salt content (2%) of the water infiltrating in the polder area is slighter higher than 
those of the recharging water in the dune area (1%). During the 20th and the beginning of the 21th 
century the landscape elements do not change any longer and the considered stress periods 
depend principally from the changing withdrawal rates in the dune area. 
 
During the presentation of the simulated results the evolution of the groundwater flow and 
distribution are treated at different levels in the aquifer and in different cross-section through it. 
Because of the limited space of this abstract only a small number of selected results can here be 
shown. First, the applied finite difference grid is located and the initial conditions of the 
20th Salt Water Intrusion Meeting 
 
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simulation are described. Hereafter, a small number of results are selected so that the different 
inverse density problems can be demonstrated.  
 
FINITE DIFFERENCE GRID, INITIAL CONDITIONS AND SOME RESULTS  
The modeled area is 4.4 km on 3.5 km. The finite difference grid consists of 88 columns, 70 
rows and 12 layers. All finite difference cells have the same size. These cells have a thickness of 
2 m and a squared base plane with a side of 50 m. The evolution of the salt water distribution is 
calculated with the method of the characteristics. At the initial time one assumes that the phreatic 
aquifer was completely filled with salt water. So, eight particles per finite difference cell are 
places with a salt water percentage of 100%.  The stresses on the aquifer during the first stress 
period depend of the different landscape elements derived from the painting of Pourbus (1571) as 
described in the introduction. The duration of this stress period was chosen so that a dynamic 
equilibrium is nearly reached in the salt water distribution (see Figure 1).        
 
 
Figure 1.  The modeled area with the principal landscape elements according to the painting of 
Pourbus (1571) along with the simulated fresh water head contour lines (in white), the groundwater 
flow (vectors) and the saltwater percentage (gray scale) of layer 2 (x and y coordinates in m) 
 
In Figure 1 the simulated results are represented in a horizontal plane at level -2 m below mean 
sea level (bmsl) according to the landscape of 1571. Under the dunes the upper part of the 
phreatic aquifer was filled with fresh water. Before the western dunes there was an outflow of 
fresh and brackish water at the low water line of spring tides. The flow of fresh water from the 
eastern dune area to the eastern bank of the tidal channel was concentrated to the southern part of 
the bank which had a more permeable subsurface and a slightly steeper slow than its northern 
part. 
June 23-27, 2008 z Naples, Florida, USA 
143 
 
Figure 2.  Principal landscape elements according to the map of Wilschut (1740) along with the 
simulated groundwater flow and the saltwater distribution in layer 2 
 
During the 17th Century the tidal channel silted up. First, the eastern dunes grew towards the 
west resulting in a larger fresh water lens under these dunes. The deepest part of the channel 
moved towards the west and the channel became shallower. Due to this the slope of the western 
bank of the tidal channel decreased while the slope of the eastern bank increased. On the 
southern part of the eastern bank there was an important fresh water flow from the eastern dunes 
toward the low water line. Above this fresh water flow there was a large salt water lens. This 
density inversion developed in a similar way as the density inversion described by Vandebohede 
& Lebbe (2006). In the second half of the 17th Century there was an erosion of the feet of the 
eastern dunes and the high water line moved toward the east. Finally, this resulted in a tidal flat 
area in the upper right part of the modeled area (Fig.2) whereas the low water line of the North 
Sea retreated to the upper right corner of the modeled area. In this tidal flat area there were still 
remains of the fresh water lens of the former eastern dunes and also of the density inversion 
under the former eastern bank of the tidal channel. Because the hydraulic gradients under the 
tidal flat area are very limited, there was only a density dependent very slow flow due to the 
inversed distribution of salt and fresh water (Fig.3). In the beginning of the 18th Century the 
polders in the lower left part of the modeled area were enlarged by the construction of the Saint 
Paul’s dyke. Due this reclaim of the former tidal flat a very slow freshening process started in the 
top of the phreatic aquifer.   
 
DISCUSSION AND CONCLUSIONS 
The historical evolution of the salt-water distribution around the Zwin estuary mouth results in a 
large number of different inverse density problems. The evolution of one of these inverse density 
problems is shown above. A detailed study of these inverse density problems along with present 
20th Salt Water Intrusion Meeting 
 
144 
day observation in area which show similar evolution as around the Zwin estuary mouth will be a 
future challenge in the salt water intrusion research.     
 
 
Figure 3.  Simulated evolution of the remains of a fresh water lens of the eastern dunes and of the 
density inversion under the eastern bank of the tidal channel after the change of the area to a tidal 
flat area in the beginning (above) and at the end (below) of the 18th Century in a cross section along 
the row (x=4225 m) 
 
REFERENCES  
Lebbe, L. & Oude Essink, G., (1999) Section 12.11. MOC DENSITY / MOCDENS3D-code. p. 434-439, in Chapter 
12. Survey of Computer codes and Case Histories, Eds. Sorek, S. & Pinder, G.F. in: Seawater Intrusion in Coastal 
Aquifers, Concepts, Methods and Practices. Eds. Bear, J., Cheng, H-D, Herrera, I., Sorek, S. and Ouazar D. 
Kluwers Academic Publishers 
Vandenbohede, A. & Lebbe, L. (2006). Effects of tides on a sloping shore: groundwater dynamics and propagation 
of the tidal wave. Hydrogeology Journal, 15 (4): 645 – 658 
 
Contact Information:  Luc. C. Lebbe, Ghent University /Geology & Soil Science Department, Krijgslaan 281, 
B9000 Gent, Belgium, Phone & Fax: 32-92644635, Email: luc.lebbe@ugent.be 


Modeling of historical evolution of salt water distribution in the phreatic aquifer in and around the silted up Zwin estuary mouth (Flanders, Belgium)

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